Summary: In this article the authors examine "automatic folding" sunshades that coil up when not in use. From the authors' experience, it seems impossible simply to fold such a sunshade in half (i.e. coil it into exactly two loops.) The object here is to figure out how many loops can appear in the coil and to understand why.

Curtis Feist received his B.S. and M.S. from California Polytechnic State University, San Luis Obispo, and his Ph.D. (in Topology) from the University of California, Davis, under the supervision of Abigail Thompson. He is currently an Associate Professor of Mathematics at Southern Oregon University.

Ramin Naimi obtained his Ph.D. in Topology from Caltech in 1992. He has been enjoying teaching at Occidental College since 1998. He also enjoys collaborating in research, currently working on projects involving symmetry groups of graphs embedded in 3-space, and knots and links in spatial graphs.